Hello.
I would like to ask you a question about a sum in a problem I have
found in Mathematica 5.1.
The sum is the following:
Sum[(k^2 - (1/2))/(k^4 + (1/4)), {k, 1, 1000}]
I have no problems with the sum in that form, but the following one
doesn't work:
s=Sum[(k^2 - (1/2))/(k^4 + (1/4)), {k, 1, m}]
s /. m->1000
It gives a long result with hypergeometric functions. Also, it cannot
be converted to a number with N[], due to some kind of ComplexInfinity
problem. FullSimplify doesn't help, neither.
Also, if I evaluate it to Infinity, I cannot get the value symbolically
nor numerically, except if I use NSum[], that gives me the right
result, 1.
I don't know if I'm doing something wrong, it is a bug, a limitation or
whatever.
Thanks a lot for your help.
Best regards.